## Journal of Symbolic Logic

### Presburger sets and p-minimal fields

Raf Cluckers

#### Abstract

We prove a cell decomposition theorem for Presburger sets and introduce a dimension theory for $Z$-groups with the Presburger structure. Using the cell decomposition theorem we obtain a full classification of Presburger sets up to definable bijection. We also exhibit a tight connection between the definable sets in an arbitrary p-minimal field and Presburger sets in its value group. We give a negative result about expansions of Presburger structures and prove uniform elimination of imaginaries for Presburger structures within the Presburger language.

#### Article information

Source
J. Symbolic Logic, Volume 68, Issue 1 (2003), 153-162.

Dates
First available in Project Euclid: 21 February 2003

https://projecteuclid.org/euclid.jsl/1045861509

Digital Object Identifier
doi:10.2178/jsl/1045861509

Mathematical Reviews number (MathSciNet)
MR1959315

Zentralblatt MATH identifier
1046.03019

#### Citation

Cluckers, Raf. Presburger sets and p-minimal fields. J. Symbolic Logic 68 (2003), no. 1, 153--162. doi:10.2178/jsl/1045861509. https://projecteuclid.org/euclid.jsl/1045861509

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